CN113538914A - Curved surface fitting algorithm with radial basis network as core - Google Patents
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Abstract
The invention discloses a curved surface fitting algorithm with a radial basis network as a core, which comprises the following steps: designing a model of a radial basis network for fitting; solving a speed distribution curved surface on the current time-distance space according to a model learning algorithm; and calculating the space-time average speed of the road section. The method limits a research object to a road section, fully utilizes the space-time distribution rule of traffic flow speed on the road section, approaches real speed distribution by utilizing discrete sampling points through a modeling method, enables the real speed distribution to be more suitable for urban road network traffic state calculation, utilizes experiments to carry out analysis and demonstration, aims at the defect that the calculation is not accurate and has weak generalization capability when a short-time traffic problem is sudden in the existing traffic state calculation method, improves an algorithm, and enables the algorithm to have stronger robustness.
Description
Technical Field
The invention relates to the technical field of urban road network traffic state calculation, in particular to a curved surface fitting algorithm with a radial basis network as a core.
Background
In recent years, with the acceleration of the urbanization process of China, the number of motor vehicles in large and medium cities rises linearly, and congestion becomes a difficult problem which needs to be faced by city development. According to statistics, about two thirds of cities in China have different congestion phenomena on main roads in the morning and evening. As far as present, Intelligent Traffic System (ITS) is the most common tool for solving the problem of road congestion. The method integrates the technologies of data acquisition, transmission, analysis and the like, fully excavates the existing traffic information, and provides powerful guarantee for relieving traffic jam, planning a travel route, scheduling vehicles and the like. At present, the coverage range of the data acquisition technology of the ITS is limited, so that the obtained traffic data is not perfect. In recent years, with the push of floating cars (buses, taxis, and the like with onboard GPS devices) and the popularization of smart phones, GPS technology has been widely used in ITS.
At present, a large number of documents already exist at home and abroad to make abundant research work on the floating car technology. However, the data base of most research is high frequency GPS data. However, in practice, due to the problems of hardware conditions, investment cost and the like, low-frequency sampling by using a floating car is more common, and a taxi system is taken as a main representative, so that how to effectively mine information of the data is a problem worthy of research. At present, the solution of the road average speed is the main means for calculating the road traffic state. The short-time (5-15 min) road traffic state calculation can provide a real-time road detection result for a user, so that the user experience is improved, and the general calculation time is not more than 15 minutes. However, the shorter the calculation cycle is, the traffic state has stronger randomness, so that the short-time road traffic state calculation provides higher challenges on a road matching technology and a road traffic state calculation method compared with the conventional floating car technology.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a curved surface fitting algorithm with a radial basis network as a core, which can effectively solve the problems in the background art.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a surface fitting algorithm taking a radial basis network as a core is characterized by comprising the following steps:
step S1, designing a model of a radial basis network for fitting, designing a network model with an n-m-S structure, namely the network model has n inputs, m hidden layer nodes and S outputs, taking a two-dimensional vector consisting of time and distance as an input vector, solving a corresponding speed scalar according to the number of taxi GPS in a time period, and finally fitting a curved surface according to a function distributed by the radial basis network;
step S2, solving a speed distribution curve surface on the current time-distance space according to a model learning algorithm, wherein the speed distribution curve surface mainly comprises three aspects of determination of a central point, determination of radial basis network width and a weight correction algorithm;
and step S3, calculating the space-time average speed of the road section, wherein the calculation is mainly carried out according to the combination of two dimensions of time and space.
Further, in step S1, the function of the radial basis network distribution is:
wherein phi (-) is a radial basis function, | | x-cjI is the Euclidean distance, cj(cj∈RR) Being the center of the radial basis network,
is the radial base network radius.
Further, in step S2, solving the velocity profile in the current time-distance space mainly includes three aspects:
(1) the determination of the center point, the selection of the radial basis network center is the key for successful use in practice, and the commonly used selection algorithm for determining the radial basis function center is as follows: selecting a radial basis network center by a random algorithm, selecting the radial basis network center and a fixed radial basis network center point by cluster learning, and calculating the radial basis network center point by the center point in a self-adaptive manner according to the length of a road section and the calculation time interval so that the radial basis network center points are uniformly distributed on a space-time plane;
(2) the method for determining the radial basis network width comprises a fixed value method and an average distance method, wherein the fixed value method is selected as a network width determination algorithm in the scheme, and the radial basis network width can be determined according to the method
Determining, wherein L is the euclidean maximum distance between all centers, and m is the number of radial basis network centers;
(3) and the weight correction algorithm adopts a gradient descent algorithm to correct the weight, and because the center point is adaptive to the road, the weight is only required to be adjusted in each iteration.
Further, in step S3, the average velocity is calculated mainly from the calculation of two dimensions of time and space, and the space-time average velocity is calculated as follows:
wherein,
and finally calculating the space-time average speed of the road section by the curve fitting algorithm.
Compared with the prior art, the invention has the beneficial effects that:
the invention limits the research object to the road section, fully utilizes the space-time distribution rule of the traffic flow speed on the road section, approaches the real speed distribution by utilizing discrete sampling points through a modeling method, so that the method is more suitable for the urban road network traffic state calculation, and utilizes experiments to analyze and demonstrate, thereby improving the algorithm and ensuring that the algorithm has stronger robustness aiming at the defect that the calculation is not accurate and has weak generalization capability when the short-time traffic problem is sudden by the existing traffic state calculation method.
Drawings
FIG. 1 is a schematic view of a radial basis network model of the present invention;
FIG. 2 is a schematic diagram of the location of the center function of the present invention;
FIG. 3 is a schematic diagram comparing the present invention with other algorithms;
FIG. 4 is a diagram illustrating the comparison between the fitting result of the present invention and the real result;
FIG. 5 is a schematic flow chart of the steps of the present invention;
FIG. 6 is a schematic diagram of the distribution of the sampling points in the time-distance space according to the present invention;
FIG. 7 is a schematic view of a camera capture scene according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In this embodiment, each road segment corresponds to a series of GPS data through a map-map matching algorithm. How to restore the traffic state of each road segment in the road network by using the information of the sampling points becomes an important problem to be solved next, and the research object is changed into all road segments contained in the urban road network by the GPS data. The method based on function fitting and the method based on vehicle tracking in the work foundation of the predecessors show good performance on the traffic state calculation problem.
The vehicle tracking method fully considers the conditions of road network topological state, signal lamp control and other factors in the road speed calculation process. Most vehicle tracking algorithms therefore exhibit good accuracy. However, for the beijing city, the five-ring in-home trunk network is composed of tens of thousands of road segments, and in this case, the calculation overhead of the vehicle tracking method is too large to be sufficient to meet the demand of short-time calculation. In contrast, methods based on function fitting have short calculation times and still achieve sufficient accuracy. The past defines a virtual physical quantity, namely the space-time average speed of the road section, which is used for representing the traffic state of the road section instead of the traffic flow, the travel time or other scalar quantities. In 2013, a large number of experiments are performed on the basis of urban road networks by the proposed curve fitting algorithm and the vehicle tracking algorithm based on shortest path search, and the accuracy of traffic state evaluation in a short-time state is compared. Experiments show that the curve fitting algorithm has strong advantages in short-time large-scale urban road network traffic state calculation. However, the surface fitting function adopted by the algorithm is a cubic surface function, an overfitting phenomenon is easily caused in the calculation process, and although some function terms in the cubic function are abandoned according to the number of sampling points of each road through an experimental result, the algorithm does not have generalization capability. Meanwhile, the algorithm is susceptible to short-time burst conditions, so that the numerical value is inaccurate.
Therefore, on the basis of the work, a surface fitting algorithm with a radial basis function network (RBFNN) as a core is provided for calculating the traffic state of the urban road network. The method limits a research object to a road section, makes full use of the space-time distribution rule of traffic flow speed on the road section, approximates real speed distribution by using discrete sampling points through a modeling method, so that the method is more suitable for urban road network traffic state calculation, and analyzes and demonstrates by using experiments.
The researched interior of a single road section shows a strong continuous property of the traffic flow. In terms of time, the traffic condition of the road in the daytime is complex, the speed of the road is low in the morning and evening, the speed of the road is high in the off-peak period, and the speed of the road is high in the evening. The speed change of the vehicle is influenced by objective rules, and the sudden vehicle stop is also a rapid change of the acceleration, has continuity in the speed distribution and keeps smooth. From the space perspective, vehicles on the road section are influenced by the traffic signal lamps at the upstream inlet and the downstream outlet, the speed of the vehicles with lower average speed is influenced by the traffic signal lamps at the road inlet and the road outlet at lower average speed, and the speed of the vehicles in the middle of the road section is stable and higher. Therefore, according to the characteristics of the traffic flow in time and space, the abstract road speed can be placed in a three-dimensional space with three dimensions of time, space and speed by using the idea of regression analysis in machine learning. And (3) obtaining the distribution states of the speed and different positions on the road section at each moment by regression in a curved surface fitting mode, and finally forming a linear three-dimensional curved surface. And integrating the linear curved surface to obtain an average value, and calculating the space-time average speed of the road section. The complex road section average speed solving problem is converted into the logical curved surface solving problem, and the calculation difficulty is simplified.
For this reason, the sampling points on the same road section need to be further processed, the time and space data of each sampling point are matched with the longitude and latitude coordinates of the road section, the time and space data are converted into two characteristic attributes of the time of entering the road section and the distance from the entrance of the road section, and the time-distance space of the road section is constructed according to the two-dimensional vector, as shown in fig. 6, the distribution condition of all sampling points in the space in one day is shown.
It has been proposed in the past to use a cubic function to fit a curved surface as a model of the vehicle's velocity distribution. The function expression of the surface fitting is as follows:
then solving the coefficients in the functional expression by using a least square method:
the surface fitting algorithm based on the cubic function has a good fitting effect in the face of a road section with short length and single road passing state. However, due to the limitation of the expression ability of the function itself, it is difficult to achieve effective fitting under the condition of long road sections or complicated road section changes. Meanwhile, the curved surface function is easy to over-fit under the condition of less sampling points. The overfitting prevention is necessarily to reduce the number of terms in the polynomial according to the experimental result, but the reduced formula obtained by the experiment is difficult to satisfy all roads. If the original fitting Function is replaced by a Radial Basis Function Neural Network (RBFNN), the problem is well solved. The RBFNN model is used for replacing the original cubic function so as to enhance the robustness of the surface fitting algorithm on the problem solving of the traffic state.
As shown in fig. 1-5, the present invention provides a surface fitting algorithm with a radial basis network as a core, comprising the following steps: step S1, designing a model of a radial basis network for fitting; step S2, solving a speed distribution curved surface on the current time-distance space; and step S3, calculating the space-time average speed of the road section.
In step S1, the model structure of the radial basis function neural network has been described in detail, and the network is a three-layer feedforward network with a single hidden layer proposed by Moondy and Darken in the end of the 80 th 20 th century. RBFNNs are widely used in numerous fields, mainly based on the following advantages: (1) the representation is simple and does not add much complexity even for multivariable inputs. (2) And radial symmetry. (3) The smoothness is good, and any derivative of order exists. (4) The basic function is simple in representation and good in resolution, so that the theoretical analysis is facilitated. After the linear inseparable mode of the original space is processed by the hidden layer, the linear inseparable mode is converted into a new high-dimensional space to become linear separable, and linear classification is realized by the output layer. The radial basis functions include a gaussian function, a multi-quadratic function, an inverse multi-quadratic function, a thin-plate spline function and the like, and all of them have good approximation capability. The fitting function in the original algorithm can be completely replaced according to the advantages of the method. The scheme designs a network model with an n-m-s structure, namely the network model has n inputs, m hidden layer nodes and s outputs, a two-dimensional vector consisting of time and distance is taken as an input vector, and if the taxi GPS data of a certain road section in the time period is i in total, the taxi GPS data can be expressed as follows: x is the number ofi＝(ti，di )That is, n in the network takes a value of 2, as shown in fig. 1, a corresponding speed scalar is obtained according to the number of taxi GPS in a time period, Σ in an output layer node indicates that a neuron in the output layer adopts a linear activation function, m takes a value determined by a calculation time interval and a road segment length, and { ω {, where ω isj: j is 1, …, m is an output weight matrix, and the output is weighted by all center point output valuesAnd, i.e. the current input value xiAnd finally, fitting a curved surface according to a function distributed by the radial basis network, wherein the function distributed by the radial basis network is as follows:
wherein phi (·) is a radial basis function, the scheme adopts a Gaussian function, | | x-cjI is the Euclidean distance, cj(cj∈RR) Being the center of the radial basis network,
for the radial basis network radius, we uniformly distribute this central function on the spatio-temporal plane when fitting the curve, placing one central function every 100m from the road entrance and one central function every 60s on the spatial scale. I.e. 54 centre function positions are needed for the calculation of an average velocity over a length of 800m, 5min as shown in figure 2.
For all road sections, the fitting curved surface based on the radial basis network with the time space interval as the reference has good fitting effect, the function item in the original cubic function needs to be increased or decreased according to the number of sampling points of each road section in the experiment process by the original algorithm, and the improved radial basis network curved surface fitting algorithm can present good curved surface fitting effect on the road section and has remarkable generalization capability as long as the center point of the radial basis network corresponding to the response is generated according to the length of the road section and the calculation time interval.
In step S2, solving the velocity distribution curve in the current time-distance space according to the model learning algorithm mainly includes three aspects:
(1) the determination of the center point, the selection of the radial basis network center is the key for successful use in practice, and the commonly used selection algorithm for determining the radial basis function center is as follows: selecting a radial basis network center by a random algorithm, selecting the radial basis network center and a fixed radial basis network center point by cluster learning, and calculating the radial basis network center point by the center point in a self-adaptive manner according to the length of a road section and the calculation time interval so that the radial basis network center points are uniformly distributed on a space-time plane;
(2) the method for determining the radial basis network width comprises a fixed value method and an average distance method, wherein the fixed value method is selected as a network width determination algorithm in the scheme, and the radial basis network width can be determined according to the method
Determining, wherein L is the euclidean maximum distance between all centers, and m is the number of radial basis network centers;
(3) the weight correction algorithm adopts a gradient descent algorithm to correct the weight, only the weight needs to be adjusted in each iteration due to the self-adaption of a center point and a road, the scheme adopts the gradient descent algorithm to correct the weight, and the weight is recorded by eiFor the error signal in the training of the ith sample, viAssuming that the number of center functions is m, for the instantaneous velocity corresponding to the sample, the formula is:
to minimize the objective function, the amount of modification of the parameter should be proportional to its negative gradient, i.e.:
the specific calculation formula is as follows:
the objective function is the sum of errors caused by all training samples, the derived parameter correction formula is a batch type adjustment, and when the error precision meets the requirement, the training is completed.
In step S3, the average speed is calculated mainly from the calculation of two dimensions of time and space, and the space-time average speed is calculated as follows:
wherein,
the method is used for calculating the road space-time average speed of the road from the perspective of actual road space-time continuity, and has high accuracy and robustness.
The following description is provided by combining comparison between a curve fitting algorithm based on a radial basis network and other algorithms, here, a road section near an airport high speed is selected as a research object, the average speed of the road section from nine points to nine points in half every five minutes is calculated, the calculation method is a method for calculating the average speed of sampling points, a curve fitting traffic state calculation method based on a cubic function, a curve fitting traffic state calculation method based on the radial basis network, and an experimental result is shown in fig. 3. This highway section sampling point distributes comparatively evenly, and the road grade is higher, and is comparatively unobstructed during the early peak, but can reflect urban road's general state. From the calculation results in the figure, it can be seen that certain errors exist in the results of different algorithms, but the variation trend of the average speed of the road section can be basically reflected.
And selecting an early peak period from 7 points to 7 points and 5 points in 6 days of 2 months and 6 months in 2013 from the database, and performing surface fitting operation on 68 sampling points of a road section. The curved surface representation capability of the RBFNN curved surface fitting algorithm is more abundant, and both the RBFNN curved surface fitting algorithm and the RBFNN curved surface fitting algorithm reflect the characteristics of the traffic flow of the road section. The calculation results at this time are shown in the following table:
the result shows that the cubic surface fitting and the RBFNN surface fitting both have good performance on a smooth road section. Then, the speed values of all sampling points in one minute in the previous test are set to be 0 to simulate the traffic paralysis of the road section under the emergency condition, and the normal traffic is recovered immediately.
By re-fitting the surface, it can be observed that the 0 samples have affected the surrounding samples due to the one minute paralysis. The RBFNN surface fitting algorithm has better fault-tolerant capability, the 0 value sampling point does not influence the fitting effect of the surrounding road state completely, and the calculation result is shown in the following graph:
therefore, the RBF has better processing capability and stronger robustness for short-time sudden traffic problems.
Although similar performance is exhibited in comparison with other algorithms, it is still important to obtain the true road section condition. It can help us to further verify the accuracy of the algorithm, for which we set an experimental scenario on a one-way road as shown in fig. 7 below. The vehicles in the picture are captured by the cameras, and the instantaneous speed of the same vehicle in different cameras is tracked and calculated. The situation that the four cameras capture the same taxi is t0,t1,t2,t3The contents shot by the cameras of the locations.
To calculate the instantaneous speed of the vehicle captured by each camera, we take the following approach to take the image point t0The video data shot at the location is taken as an example. Tying red silk ribbons on a fence in the middle of a bidirectional road as a mark, and recording the time t of a vehicle passing through a front marker and a rear marker0' and t0", the spacing between the two markers was 9 meters. The position of the cameras is between two markers, the interval between each camera is 60 meters, namely, the 240-meter range of the single-line road section is monitored as an experimental road section, and the shooting time is takenFrom 16:00 to 16: 30. We will t0' and t0"average value of" is denoted as t0From this we can also get t1,t2,t3And the corresponding instantaneous speed v0,v1,v2,v3. That is, each vehicle passing the one-way road segment on the side can obtain 4 sampling points. Where the vehicle true travel time is t3-t0And the travel distance is 180m, the average speed of the individual vehicles can be known. And averaging all recorded instantaneous speeds within 5min to obtain the real speed of the road section in the time period. A vehicle which appears in four cameras simultaneously and can clearly distinguish the appearance is used as a floating vehicle, a plurality of pieces of data are obtained in total, and recording is carried out according to the following format.
The comparison result between the result tested by the radial basis network surface fitting algorithm and the true value is shown in fig. 4, and the calculation result in the graph shows that the radial basis network surface fitting algorithm has errors with actual data, but the variation trend is basically consistent, the radial basis network surface fitting algorithm has a good experimental effect, and the algorithm has higher accuracy.
And aiming at the distribution regularity of the speed of the road section on the time-space layer, introducing the idea of surface fitting and solving the space-time average value of the road section. And then, according to the original cubic surface fitting algorithm, an improved RBFNN-based surface fitting algorithm is provided. In the experiment, the main research object is locked as a one-way road section, and the feasibility of the algorithm is verified by comparing with other algorithms. The robustness of the algorithm is verified by examination of extreme data. And finally, comparing the speed with the actual road speed shot by the camera, and verifying the accuracy of the RBFNN curved surface fitting algorithm. The RBFNN-based surface fitting algorithm can be verified to have good performance in calculating the road traffic state.
Compared with the prior art, the technical scheme limits the research object to the road section, fully utilizes the space-time distribution rule of the traffic flow speed on the road section, approaches the real speed distribution by utilizing discrete sampling points through a modeling method, so that the method is more suitable for the urban road network traffic state calculation, utilizes experiments to analyze and demonstrate, aims at the defect that the calculation is not accurate and has poor generalization capability when the short-time traffic problem is sudden in the existing traffic state calculation method, and improves the algorithm so that the method has stronger robustness.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (4)
1. A surface fitting algorithm taking a radial basis network as a core is characterized by comprising the following steps:
step S1, designing a model of a radial basis network for fitting, designing a network model with an n-m-S structure, namely the network model has n inputs, m hidden layer nodes and S outputs, taking a two-dimensional vector consisting of time and distance as an input vector, solving a corresponding speed scalar according to the number of taxi GPS in a time period, and finally fitting a curved surface according to a function distributed by the radial basis network;
step S2, solving a speed distribution curve surface on the current time-distance space according to a model learning algorithm, wherein the speed distribution curve surface mainly comprises three aspects of determination of a central point, determination of radial basis network width and a weight correction algorithm;
and step S3, calculating the space-time average speed of the road section, wherein the calculation is mainly carried out according to the combination of two dimensions of time and space.
2. A radial basis network centric surface fitting algorithm according to claim 1, wherein in step S1, the function of the radial basis network distribution is:
where Φ (-) is the radial basis function, | | x-cjI is the Euclidean distance, cj(cj∈Rn) Being the center of the radial basis network,
is the radial base network radius.
3. A radial basis network-centric surface fitting algorithm according to claim 1, wherein in step S2, solving the current time-distance space velocity distribution surface mainly includes three aspects:
(1) the determination of the center point, the selection of the radial basis network center is the key for successful use in practice, and the commonly used selection algorithm for determining the radial basis function center is as follows: selecting a radial basis network center by a random algorithm, selecting the radial basis network center and a fixed radial basis network center point by cluster learning, and calculating the radial basis network center point by the center point in a self-adaptive manner according to the length of a road section and the calculation time interval so that the radial basis network center points are uniformly distributed on a space-time plane;
(2) the method for determining the radial basis network width comprises a fixed value method and an average distance method, wherein the fixed value method is selected as a network width determination algorithm in the scheme, and the radial basis network width can be determined according to the method
Determining where L is the Euclidean distance between all centersOff, m is the number of radial base network centers;
(3) and the weight correction algorithm adopts a gradient descent algorithm to correct the weight, and because the center point is adaptive to the road, the weight is only required to be adjusted in each iteration.
4. A radial basis network centric surface fitting algorithm according to claim 1, characterized in that, in step S3, the average velocity is calculated mainly from the calculation of two dimensions of time and space, and the space-time average velocity is calculated as follows:
wherein,
and finally calculating the space-time average speed of the road section by the curve fitting algorithm.
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| CN102737508A (en) * | 2012-06-19 | 2012-10-17 | 银江股份有限公司 | Urban road traffic state detection method combined with support vector machine (SVM) and back propagation (BP) neural network |
| CN103853044A (en) * | 2012-12-04 | 2014-06-11 | 中山大学深圳研究院 | Interactive group control method based on radial basis function |
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